Gotcha. It does make sense.
In that case, I would send an additional parameter with the JSON response of whether or not a day is blocked (which is calculated on the server side).
You can use the dayRender callback to change the color of a particular day based on the blocked days. Depending on how you are allowing new event creations, you would want to handle the validation there as well as the backend on the model.
This does get a bit tricky since you're having to validate on server side and render on client side as well.
Also check out this JSFiddle where they're adding a class to a date, dynamically, after the calendar is rendered.